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FiReaNGeL writes "Scientists have for the first time observed a nanoscale symmetry hidden in solid state matter. 'In order to study these nanoscale quantum effects, the researchers have focused on the magnetic material cobalt niobate. It consists of linked magnetic atoms, which form chains just like a very thin bar magnet, but only one atom wide.' By artificially introducing more quantum uncertainty, the researchers observed that the chain acts like a nanoscale guitar string. The first two notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618, which is the golden ratio famous from art and architecture. The observed resonant states in cobalt niobate are a dramatic laboratory illustration of the way in which mathematical theories developed for particle physics may find application in nanoscale science and ultimately in future technology."

Although I agree that in this context 'redundant' was a lame mod. However, 'redundant' doesn't mean "already posted in this thread". I know I'm being pedantic, and I apologize for that, but we see so many memes here that I cannot believe anybody would still be confused about what 'redundant' means. A first post in a thread about Nexus One that says "why doesn't Google just make a phone that is just a phone without all the bells and whistles?!?!" is 'redundant'.

The golden ratio phi is "the most irrational number", in some sense. If you try to take better and better rational approximations to phi, obviously you need to go to bigger and bigger denominators in the fraction. In the limit as the error tolerance goes to zero, the necessary size of the denominator grows at a certain asymptotic rate. One can show [ams.org] that for phi this rate is the largest possible, so the golden ratio is the hardest number to rationally approximate.

if you ask me the deity that needs to constantly fiddle with the universe to make things go its way isn't very intelligent after all. a real show of intelligence would be to interact as little as possible and yet have the universe with its simple, derivable nature inexorably lead toward whatever said deity had in mind.

People too often conceive of a personal, immanent God concerned with the world in terms of temporality that, as you say, makes it seem as if God has to continually fiddle with the world to make it go. But God continually eludes human conception, and if God in some sense stands outside of time, then from the viewpoint of time the eternal act of creation appears to be either strung out throughout all time, or repeated continually. In reality, however, if God stands outside of time then the only real way to de

The real question is, can anything in the quantum world really involve a non-rational number (or even a non-terminating decimal)?

Take a simple circle. A mathematical perfect circle is effectively a polygon with an infinite number of sides, and pi is infinite because of this same fact. A 'circular' object in the real universe has faceted sides, each of at least the lengths between adjacent atoms. (It's also 'fuzzy' when measured at that scale, and part of that is also QM). The whole concept of Planck length

A measurement cannot have such great precision that the inaccuracy in the measurement is shorter than the plank length.

That is not known to be the case. Got a reference for that?
It's also something entirely different from suggesting that space is discretized in Planck-length units, which is certainly not the case. In fact, it's a fundamental postulate of QM that the wave function is smooth and continuous (and hence, so is the location-probability distribution). If it wasn't continuous, then you'd end up

I never said that smaller length scales couldn't exist, just that they could not effectively be distinguished through measurement according to our current knowledge of physics. The restriction may be sidestepped if gravity acts in a different manner at such extremely small length scales than it does it larger scales. A smaller value for G would effectively decrease the size of the plank scale as an example. However, at the current time, physics as we know it does not allow for measurements to be made that are of greater precision.

At this point in the discussion there is a need to remind everyone that this level of physics is appropriate to describing models of the Universe. But, as pointed out by the luminaries who formulated the Copenhagen convention, the Universe is not the model, and the human mind is fundamentally incapable of comprehending how the models we construct differ from the Universe.

Not only do we not know what is really going on, we cannot possibly ever know that; it is one of the limitations that make us humans rather than gods. But we can make models that are fun to play with, and sometimes lead to new insights. Or even new gadgets, like computers, the Internet, slashdot...

I can't believe I used to think that what I thought was happening was really going on --The Sugar Beets

First, as you point out, it is a postulate. Not an assumption. And therefore not subject to evidentiary proof. Although it is certainly falsifiable.

Second, I lack the time to do the training (estimate about ten years culminating in PhD in physics level mentation) to understand the kind of evidence involved. Further, I probably lack the intellect to handle that evidence properly: I did not do well in calculus. Additionally, I also lack the skills that would be needed to communicate such evidence to persons

That seems a little rash considering how new and undeveloped all of the ideas about quantum gravity are, especially some recent quantum gravity work such as Causal dynamical triangulation and newer work. Some of these ideas indicate that the third spatial dimension, time, and the linearity of quantum mechanics are emergent at the Plank scale.

You are mistaken. There is no fundamental limit (at least, according to known theory) on the precision of a measurement of the position. The only limit is on how well you can simultaneously measure the position and the momentum. The "plank length" is nothing more than a convenient choice of units.

The real question is, can anything in the quantum world really involve a non-rational number (or even a non-terminating decimal)?

Take a simple circle. A mathematical perfect circle is effectively a polygon with an infinite number of sides, and pi is infinite because of this same fact. A 'circular' object in the real universe has faceted sides, each of at least the lengths between adjacent atoms. (It's also 'fuzzy' when measured at that scale, and part of that is also QM). The whole concept of Planck length dictates minimum distances, angles and such, and objects have granularity that means an infinite number of facets or an infinitely dividable curve isn't part of the real universe.

So, isn't what's been discovered here an expression of the golden ratio to only some finite number of decimal places?

Reality is not "granular" in the sense of being divided into fixed-size chunks. It is like you said, fuzzy. The Planck length is just the guaranteed minimum amount of fuzz that everything has... at that scale you don't have surfaces at all, just "most of the fuzz is gone by around here"

In this particular case I suspect they're actually talking about the atoms in these string flipping between spin-up and spin-down, rather than anything actually moving through space like an actual guitar string, so what reall

"The whole concept of Planck length dictates minimum distances, angles and such, and objects have granularity"

You have been misinformed but it's a common misconception. The Plank length is the base unit for a system of units derived from physical constants, geometries smaller than the PL are where GR theory stops working and QM takes over. That the dividing line between our two best models of the universe should be expressable using nothing but physical constants is quite remarkable and it's probably telling us something we don't yet comprehend. Or as Heisenberg is alleged to have put it; "more fascinating than watching a monkey shit a grandfather clock." [cracked.com]

As the others pointed out, most physicists are pretty sure that space and time should be quantized, but it's not a certainty yet.

Assuming that space is quantized, you're right - the closest you could ever really come is approximating the golden ratio.

A nonterminating decimal could be represented if you had a situation where division makes sense. 4/3 is a nonterminating decimal, but both 4 and 3 are perfectly reasonable values in a quantized system.

Yes, there will certainly be an error involved here. However, the bigger question is whether we'll have accurate enough measurements to actually find this error. I'll bet that measurement accuracy will be a problem with this long before you run into problems with a quantized universe.

Incorrect. The plank length is the smallest region in space that can theoretically be measured. A photon with a short enough wavelength to take a measurement of anything shorter than the plank length will collapse upon its self as a newly formed black hole. It is the fundamental limit to known physics and is effectively the granularity of space its self.

the researchers have focused on the magnetic material cobalt niobate. It consists of linked magnetic atoms, which form chains just like a very thin bar magnet, but only one atom wide and are a useful model for describing ferromagnetism on the nanoscale in solid state matter.

Our computer memory technologies are largely based on understanding magnetizable materials at a very short length scale. The next logical step is to understand various phenomena of these materials at the nanoscale which is exactly wha

Given the way the U.S. of A. works, I would not be surprised to see first use in the strip on people's credit cards in order to store your last 10,000 purchases. Coupled with an RFID chip, this would enable targeted advertising as you walked down the street...and voila! We have Blade Runner.

Sans exotic feminine androids, of course; we always seem to get the bad out of Sci-Fi first.

As a (former) mathematician, I would like to point out that the ratio really comes from elementary (pun intended; read on to find out more) geometry. The ancient Greeks played around with it quite a lot and Euclid mentioned it (more or less) in his Elements [clarku.edu]. The Greeks weren't interested in this because of art or how pretty it was, but because they were particularly crazy about geometry (nearly all of their mathematics was derived from it) and some seemed to think that the universe could be understood through geometry alone. Anyway, it is just the fairly simple ratio of lengths of two lines such that the ratio between the larger and the smaller is the same as the ratio of them both added and the larger, or algebraically;

(a + b)/a = a / b = phi

This can then be trivially rearranged into phi^2 - phi - 1 = 0, and then that has the one positive solution; phi = [1 + sqrt(5)]/2 (the negative solution being [1 - sqrt(5)]/2 = - 0.618... but negative lengths and ratios tend to prove problematic). As usual, Wikipedia has more information. [wikipedia.org]

While it is quite interesting to see it appear in a quantum mechanical setting, it isn't particularly shocking (to me). The number is the result of a fairly simple equation (as shown above) which is why it seems to appear so frequently in nature. While I didn't get this far in my studies of quantum theories, it wouldn't surprise me if, once the mathematicians have a chance to look into this, the reason behind this appearance of phi is found to be rather trivial.

However, I am not a physicist, or an expert in this field, so I may be completely wrong.

How do you stop being a mathematician? (you don't seem to have stopped).

By being forced to graduate from university and getting caught up in politics [pp-international.net] and law [pirateparty.org.uk]. It must be at least 3 months since I did any proper maths (and the stuff above doesn't count - any suitably well-taught 8 year-old should be able to derive the answer; and it is all on Wikipedia anyway). But still, I guess one never quite recovers from spending 5+ years almost entirely devoted to the subject...

How do you stop being a mathematician? (you don't seem to have stopped).

By being forced to graduate from university and getting caught up in politics [pp-international.net] and law [pirateparty.org.uk]. It must be at least 3 months since I did any proper maths (and the stuff above doesn't count - any suitably well-taught 8 year-old should be able to derive the answer; and it is all on Wikipedia anyway). But still, I guess one never quite recovers from spending 5+ years almost entirely devoted to the subject...

Wish people would stop fussing that college actually makes them learn things outside their field of study.If you get through college and don't understand why they made you take those classes you missed the point of college and need to go back because you still have a LOT more to learn about the world.

While it is quite interesting to see it appear in a quantum mechanical setting, it isn't particularly shocking (to me). The number is the result of a fairly simple equation (as shown above) which is why it seems to appear so frequently in nature. While I didn't get this far in my studies of quantum theories, it wouldn't surprise me if, once the mathematicians have a chance to look into this, the reason behind this appearance of phi is found to be rather trivial.

Yes, it's more the other way around really. The fact that the ratio between the first two frequencies measured in the spectrum was the Golden Ratio (within error), was evidence that the state had E8 symmetry, for group-theoretical reasons I can't quite explain. (I'm kind of in the opposite situation; I know QM but Group Theory was never my strongest point)

This is interesting because E8 isn't a symmetry many real physical systems have. But it's of interest for string theorists and other advanced theories, so it's interesting if they can find systems that can act as a model. The 'real' system here doesn't have E8 symmetry either. Rather it's a system of quasiparticles [wikipedia.org] created by the spins of the system which is E8, when exposed to a magnetic field at a certain critical phase-change point.

Which is why the title of the Science article calls it "emergent E8 symmetry".

Maybe what we can see is just the surface of a deeper reality, and below that something deeper again, etc. etc.. So this appearance of a golden ratio is actually an artefact of a continued fraction i.e. 1 + 1/(1+1/(1+1/(1+1/(.....

For those of you that want to hear what this ratios sounds like, it's 833 cents [mal-2.com], or a minor sixth plus 33 cents. This happens to be the interval used to form the aptly named Bohlen 833 cents (or A12) scale. [wikipedia.org]

note that golden ratio is found in many celebrated works of art. a lot of artists in history used it knowingly in their masterpieces. such pieces of art are known to appeal to human's liking more. liking, appreciation, all subjective concepts. human psyche is something we havent been able to approach with any tangible, usable definite method up to this date.

now we find this ration in quantum mechanics.

this is practically the first solid link in between something that is numeric, defined and clear cut and hu

note that pi is found in many celebrated works of art. a lot of artists in history used it knowingly in their masterpieces. such pieces of art are known to appeal to human's liking more. liking, appreciation, all subjective concepts. human psyche is something we havent been able to approach with any tangible, usable definite method up to this date.

now we find this ration in quantum mechanics.

this is practically the first solid link in between something that is numeric, defined and clear cut and human psyche.

Here's my cut at a car analogy. Notice that a naturally recurring form-factor for popular cars involves a height to length ratio of 1:1.618. That ratio shows up again in that "rise to run" ratio of windshield rake....and again in overdrive gear ratio... and yet again in...

The golden ratio is found everywhere in nature even to the quantum level. It is also the most pleasing ratio to the human eye.

It would be highly improbable for a random universe to create this sort of symmetry.

To believe in a random universe requires a lot more mental gymnastics to reconcile the observed universe with that world view.

Or it could just be that the ratio comes from a very simple geometrical idea and a pretty basic equation.

Next you'll be suggesting that the fact that so many things in the universe seem to be approximately spherical is evidence of a divine being.

Oh, and just because something is improbable, doesn't mean that it can't happen. As for it being "most pleasing to the human eye", personally, I prefer the 1:1 ratio; squares have more symmetry than rectangles.

This is not a 'high form of symmetry' but very basic one; a solution to a very rudimentary quadratic equation. I, for one am surprised we're not seeing such solutions more often around us. Here's why: every semi-dynamic system tends to find a local energy minimum, which needs to be stable. A quadratic equation has always a stable minimum or it doesn't have a minimum. Well... that's all, nothing more to see here for me.

If the bodies of most organisms are anything to go by, evolution loves symmetry. The universe isn't random, it obeys rules, and when you combine random effects with structured rules you fairly often get to see patterns.
Perhaps a better explanation:
"The golden ratio is found everywhere in nature even to the quantum level. It is THEREFORE the most pleasing ratio to the human eye.
It would be highly PROBABLE for a random universe, GOVERNED BY PHYSICAL LAWS, to create this sort of symmetry."

The golden ratio is found everywhere in nature even to the quantum level. It is also the most pleasing ratio to the human eye.It would be highly improbable for a random universe to create this sort of symmetry.

To believe in a random universe requires a lot more mental gymnastics to reconcile the observed universe with that world view.

Which is more likely:A) The human eye finds the golden ratio pleasing because it is everywhere in natureB) the golden ratio is everwhere in nature because it is pleasing to the human eye

It's okay to say "I don't know."You don't have to fill in all the gaps with "God"

What's more, no one said the universe was "random", at least not in the sense of having no rules or structure. There's just a gap between, "having rules, structure, and rationality" and "being consciously designed by a loving creator."

And then even beyond that, I don't know anyone who claimed that this universe was "probable". Maybe this universe, with all its symmetry, is highly improbable. Even highly improbable things might happen once.

You might have a point if the golden ratio were an entirely arbitrary number and not one derived from a simple geometric relation [wikimedia.org]. Pointing to the golden ratio as evidence for the existence of god is like pointing to occurrences of pi in nature, or the Fibonacci sequence. It isn't god's fingerprints, it's math's fingerprints.

What is an abstract concept like mathematics doing getting its grubby fingerprints all over physical reality? Some would say that only God could do that. Or are you trying to assert that the universe is just as abstract and unreal as the number 2, and we're trapped in it [xkcd.com]?

I believe randomness doesn't exist. In its place stands "too complicated to understand".

Take the typical state lotto. If you knew all of the variables in the machine that draws the numbers, you can solve for which numbers will land in the winning numbers area. As a result, the lottery keeps details of the machine secret. Is the ball marked 43 the same ball (with the same weight and other properties) as the 43 in the previous or next drawing? Where is the machine located and what elevation is it at? When exa

You don't understand quantum mechanics. For QM the world is fundamentally stochastic, not just pseudo random.

That's actually not quantum mechanics but rather the Copenhagen interpretation of QM.

QM doesn't actually tell us much on whether the universe is deterministic or not, because:
A) The time-evolution of the wave-function itself is deterministic.
and
B) Because it's a philosophical question Science will never be able to answer.
You can always simply deny that it's the ultimate theory of Reality
and then add a metaphysical layer explaining why it only 'appears' to be random. Or non-random.

Yet again someone who just doesn't get what QM shows.The evolution of the State Vector is unitary and therefore deterministic. That is a consequence of unitarity, as all the probabilities must add up to one. Any quantum experiment you perform can only return a probabilistic result. This is independent of whatever interpretation of QM you prefer and is not dependent on the Copenhagen Interpretation.

Einstein did not like the elimination of determinism from physical theory and believed a theory showing hidd

You picked a good authority comparison. Hawking is sort of known as a black hole guy. The same approach that rejects randomness also rejects black holes. I never paid much attention to Hawking but I would expect he was an Aristotle type while Einstein was a Platoist. So this is the real difference. And I think it is pretty easy to make fun of reductionists.

This is a nitpick, but technically the world is not stochastic but rather our perception of it is. When you run an experiment where you can't observe what's going on, it evolves in a perfect deterministic manner. Only the act of forcing an experiment that ends in multiple states to pick one of those states introduces the perceived non-determinism.

Take the typical state lotto. If you knew all of the variables in the machine that draws the numbers, you can solve for which numbers will land in the winning numbers area.

Ummmm....yeah...I'm gonna have to go ahead and disagree with you there. Most of those machines blow ping-pong balls around with air, which is most likely turbulent, and they are blown up into the slots when the lottery lady pulls the lever for the slot. Since, at a minimum, you can't solve for the state of the lottery lady, you can't "solve for which numbers will land in the winning numbers area."

(Never mind the outrageous accuracy of initial conditions and precision of the calculations you'd need to solve for the movement of ~4 dozen ping-pong balls being blown around by turbulent air.)

I believe randomness doesn't exist. In its place stands "too complicated to understand".

David Bohm wrote a lot about that, especially later in life. He essentially believed that what we perceive as randomness is a higher degree of order. An example he liked to use is a drop of ink placed in a cylindrical tank of glycerin, with a smaller central cylinder attached to a crank. If the crank is turned slowly in one direction, the drop of ink smears out and finally becomes invisible, dissolved in the surrounding medium. But if the crank is turned slowly back in the opposite direction, the drop of ink coalesces.

The unturned ink has a low (meaning simple) degree of order, while the spread-out ink has a high (complex) degree of order that is made apparent only when we wind it back to a state we can easily grasp. He also called these states the explicate, or what is readily apparent, and the implicate, or what is waiting to coalesce. The implicate order is why we have the maxim "hindsight is 20/20"--once something has happened, it often becomes easier to see how previous events lead up to this one.

It's interesting stuff, though certainly not orthodox, especially when one starts reading about the holomovement.

You are thinking about quantum mechanics backwards. The true things that exist do so in many “classical” states simultaneously, i.e. the true nature of the “particle” is really a wave. We are the quirks in the system because our wave functions are so highly entangled that we perceive the universe as if it were deterministic. When we “measure” a quantity, what we are doing is forcing something that is in many states to tell us which state it is in. However, this is act

Which brings me to the point of all this - How come only a very few scientists ever ask 'Why is this so?'.

A lot of them do, but that question isn't science, it falls into the realm of philosophy or religion. As of yet, science can't answer why, and won't be able to until "why" is reduced to a measurable property. I'm very happy that scientists aren't shoving religion or philosophy down my throat. Science is the art of observing and recording, and after a long string of this, throwing out a theory that tr

History and Philosophy of Science is nowadays an established discipline, which unfortunately isn't taken as seriously as it should be.I suppose my argument isn't with Newtonian methodology. Newton himself asked why and conclusions should normally answer Why-style questions, except in many papers today, a conclusion is a summary of the results and pointers for further research.

In some eyes, the lost science of Analogy could be of help here.If the golden ratio is apparent in the nano-scale quantum universe wh